泛函不等式及其应用(英文)  

Functional Inequalities and Applications

作　　者：王凤雨[1] 

机构地区：[1]北京师范大学数学系,北京中国100875

出　　处：《数学进展》2003年第5期513-528,共16页Advances in Mathematics（China）

基　　金：Research supported in part by NSFC(No. 10121101, No. 10025105), TRAPOYT and the 973-Project

摘　　要：本文介绍有关泛函不等式及谱理论与马氏过程研究的若干新进展.我们首先简要回顾了两个著名不等式,即Poincar不等式与对数不等式,然后分别使用泛函不等式研究本征谱、马氏半群的收敛速度和运费不等式.This paper surveys some new progress concerning functional inequalities and applications to the study of Markov processes and spectral theory. We first briefly recall two well-known inequalities, i.e. the log-Sobolev inequality and Poincare inequality, then we introduce functional inequalities to study the essential spectrum, the decay of Markov semigroups, and the transportation cost inequalities.

关 键 词：泛函不等式 谱理论 马氏过程 POINCARE不等式 对数不等式 马氏半群 本征谱 收敛速度 运费不等式 

分 类 号：O178[理学—数学] O177.7[理学—基础数学]